Question: The sum of two numbers is $88$, and their difference is $6$. What are the two numbers?
Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 88}$ ${x-y = 6}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 94 $ $ x = \dfrac{94}{2} $ ${x = 47}$ Now that you know ${x = 47}$ , plug it back into $ {x+y = 88}$ to find $y$ ${(47)}{ + y = 88}$ ${y = 41}$ You can also plug ${x = 47}$ into $ {x-y = 6}$ and get the same answer for $y$ ${(47)}{ - y = 6}$ ${y = 41}$ Therefore, the larger number is $47$, and the smaller number is $41$.